In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean
φ=0.6180339887, yielding for dark energy to matter mass fractions
. Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be
, and further the ratio of dark matter to baryonic one
. If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield
. Replacing the “
Madelung” constant α of
Villata’s “lattice universe” by
φ, one reaches again 1 +
φ as the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3
D lattice a flat 2
D one of rocksalt type, the numerical similarity between the
Madelung constant
and φ
−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number
φ may indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the
Archimedes’ constant
π, giving for
respectively for the dark components
. However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.